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Does someone know how a quadratic relationship between two latent constructs can be modelled?

Any input would be great - Thank you

Hi,

1) If VL1 is measured by three indicators (X1, X2, X3) we could create a squared VL1 measured by (X1*X1, X2*X2, X3*X3, X1*X2, X1*X3, X2*X3).
First reference: Kenny, David A.; Judd, Charles M. (1984). Estimating the Nonlinear and Interactive Effects of Latent Variables. Psychological Bulletin, Vol. 96, No. I. 201-210.
Example: p.328) KLINE, Rex. B. (2005). Principles and practices of Structural Equation Modeling. 2nd Ed. New York, The Guilford Press.
- These product terms must be computed before importing the data to SmartPLS
- It is recommended to centering the MVs before multiply them.

2) MARSH, H.W.; WEN, Z.; HAU, K. Structural Equation Models of Latent Interation and Quadratic Effects. In HANCOCK, G.R.; MUELLER, R.O. (Ed.) (2006). Structural Equation Modeling: a second course. Connecticut: IAP – Information Age Publishing, Inc.
- p.244 = Types of product indicators
- p.248 = Example using just X1*X1; X2*X2; X3*X3 as the indicators of the quadratic LV.

3) One last possibility is
- run the model without the quadratic term
- copy the standardized LV scores
- paste these scores to the original data set
- compute the LV*LV
- import the new data set to SmartPLS
- Use the LV*LV score as a single indicator to the quadratic term.

Best regards

Bido

Hi everybody,

I found a quadratic relationship in my research model using SPSS curve estimation. I want to integrate this relationship in my PLS model, now. I understand the procedures explained above (i.e. the calculation of the quadratic LVs), still I am not totally sure how to model it.

Do have to include the original variable (LV1) and the quadratic version (LVq1) of it into the model? If I do so, the effect of LV1 is negative (-.2) and the effect of LVq1 is positive (+.7). I am not sure how to interpret this.

What if LV1 is endogenous and has other effects that are linear? How do I have to model this?

It would be great if somebody could help me.

Cheers
Tobi

Bido's approach is sound.

a more exploratory approach is to use software from Buckler. Neusrel

brad